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Lesson: Slope–Intercept Form of a Line

Sample Question Videos

Worksheet • 12 Questions • 1 Video

Q1:

Calculate the gradient and the -intercept for the function .

  • A and
  • B and
  • C and
  • D and
  • E and

Q2:

Find the slope π‘š and the 𝑦 -intercept 𝑏 of this straight line.

  • A π‘š = 1 , 𝑏 = βˆ’ 1
  • B π‘š = βˆ’ 1 3 , 𝑏 = 3
  • C π‘š = 1 , 𝑏 = 1
  • D π‘š = 1 3 , 𝑏 = βˆ’ 3
  • E π‘š = βˆ’ 1 , 𝑏 = 1

Q3:

True or false: The equation of a line passing through the origin is 𝑦 = π‘š π‘₯ .

  • Afalse
  • Btrue

Q4:

Which of the following graphs represents the equation 𝑦 = 4 π‘₯ βˆ’ 1 ?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following graphs represents the equation 𝑦 = π‘₯ + 3 ?

  • A
  • B
  • C
  • D
  • E

Q6:

Write the equation that represents the linear function shown in the given table.

π‘₯ -value βˆ’ 2 βˆ’ 1 0
𝑦 -value 3 4 5
  • A 𝑦 = π‘₯ + 5
  • B 𝑦 = 5 π‘₯ + 1
  • C 𝑦 = π‘₯ βˆ’ 5
  • D 𝑦 = βˆ’ π‘₯ + 5
  • E 𝑦 = π‘₯ 5 + 1

Q7:

What is the 𝑦 -intercept of the line passing through ( βˆ’ 2 , βˆ’ 1 6 ) and ( 1 , βˆ’ 4 ) ?

Q8:

Write a linear function in the form 𝑦 = π‘š π‘₯ + 𝑐 , that has a slope of 3 and a 𝑦 -intercept of 8.

  • A 𝑦 = 3 π‘₯ + 8
  • B 𝑦 = 3 π‘₯ βˆ’ 8
  • C 𝑦 = 8 π‘₯ + 3
  • D 𝑦 = 3 π‘₯ + 1 8
  • E 𝑦 = π‘₯ 3 + 8

Q9:

True or false: The equation of a line intercepting the vertical axis at 𝑏 is 𝑦 = π‘š π‘₯ + 𝑏 .

  • Afalse
  • Btrue

Q10:

What is the relation between the point ( 0 , 4 ) and the line 𝑦 = 2 π‘₯ βˆ’ 8 ?

  • A It lies above the line.
  • B It lies on the line.
  • C It is the π‘₯ -intercept of the line.
  • D It is below the line.
  • E It is the 𝑦 -intercept of the line.

Q11:

A straight line is defined by the equation 𝑦 = π‘š π‘₯ + 𝑐 .

Given that the point ( π‘₯ , 𝑦 ) 1 1 lies on the line, find an expression for 𝑐 in terms of π‘š , π‘₯ 1 , and 𝑦 1 .

  • A 𝑦 βˆ’ π‘š π‘₯ 1 1
  • B 𝑦 βˆ’ 1 π‘š π‘₯ 1 1
  • C 𝑦 + π‘š π‘₯ 1 1
  • D π‘š 𝑦 βˆ’ π‘₯ 1 1
  • E βˆ’ 𝑦 βˆ’ π‘š π‘₯ 1 1

Given also that the point ( π‘₯ , 𝑦 ) 2 2 lies on the line and π‘š is the slope of the line, find an expression for π‘š in terms of 𝑦 1 , 𝑦 2 , π‘₯ 1 , and π‘₯ 2 .

  • A 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ 2 1 2 1
  • B 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ 2 1 1 2
  • C 𝑦 βˆ’ π‘₯ 𝑦 βˆ’ π‘₯ 2 2 1 1
  • D 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ 1 2 2 1
  • E π‘₯ βˆ’ π‘₯ 𝑦 βˆ’ 𝑦 2 1 2 1

By substituting in for 𝑐 and factorizing out π‘š , find the formula for the equation of the line.

  • A 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ ) 1 1
  • B 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ ) 1 2
  • C 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ ) 1
  • D 𝑦 βˆ’ 𝑦 = π‘š ( π‘₯ βˆ’ π‘₯ ) 2 1
  • E 𝑦 βˆ’ 𝑦 = π‘š π‘₯ 1

Substitute in your expression for π‘š to complete your formula.

  • A 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ ) 1 2 1 2 1 1
  • B 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ ) 1 2 1 2 1 2
  • C 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ ) 2 1 2 1 1
  • D 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ ( π‘₯ βˆ’ π‘₯ ) 2 2 1 2 1 1
  • E 𝑦 βˆ’ 𝑦 = 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯ π‘₯ 1 2 1 2 1

Q12:

The general form for the equation of any linear function is 𝑦 = π‘š π‘₯ + 𝑏 . What do π‘š and 𝑏 represent?

  • A π‘š represents the slope of the graph of the function, and 𝑏 represents the 𝑦 -intercept of the graph of the function.
  • B 𝑏 represents the slope of the graph of the function, and π‘š represents the 𝑦 -intercept of the graph of the function.
  • C 𝑏 represents the slope of the graph of the function, and π‘š represents the π‘₯ -intercept of the graph of the function.
  • D π‘š represents the slope of the graph of the function, and 𝑏 represents the π‘₯ -intercept of the graph of the function.
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